Supreme Court justices on Tuesday opened a floodgate of questions about a water dispute pitting Texas against Oklahoma, with the eventual outcome still in doubt.

Some questions sounded sympathetic to the thirsty Tarrant Regional Water District, which seeks Oklahoma water to serve Fort Worth-area customers. Other questions seemingly supported Oklahoma. Many questions, though, simply underscored the legal and technical complications now confronting justices dealing with what may be the biggest water law case of the year.

“You read this brief that you submitted,” Justice Elena Kagan told the Obama administration attorney at one point, “and it gives you a kind of a headache.”

At another point, Justice Antonin Scalia told a lawyer, “I don’t understand what you just said,” while Justice Sonia Sotomayor acknowledged that she “can’t make rhyme or reason” out of some provisions of a water deal. And following one drawn-out scenario that seemed to reach a dead end, Justice Stephen Breyer offered a simple one-word verbal shrug: “Anyway.”

While some of the uncertainty may have been professed, in order to make a point, it did make clear what a different world water law can be.

The practical question, simply put, is whether Oklahoma can effectively deny the Tarrant Regional Water District’s application for water under what’s called the Red River Compact. The eventual answer will help shape where Texas customers get their water from, and at what price. It will also shape what kind of clout states might have in securing water from across borders.

“When you say Texas has the right to go into Oklahoma, just think about that phrase,” a skeptical-sounding Justice Samuel Alito told Rothfeld. “That’s very striking. I mean, it sounds like they are going to send in the National Guard or the Texas Rangers.”

Oklahoma, Texas, Arkansas and Louisiana took some 25 years to negotiate the Red River Compact, signed in 1978, as a way to divvy up access to the 1,300-mile Red River, which moves from the Texas Panhandle southeast through the three other states. The compact allocates most of the water it apportions to the states in which that water is located. In certain cases, though, the compact equally divvies up water to the four participating states.

This case concerns water in an area that encompasses territory in Texas, Oklahoma and Arkansas. Tarrant argues that the compact means Texas has a right to 25 percent of the sub-basin’s water above a certain level.

Tarrant, which serves some 2 million customers in the Fort Worth area, applied for water from an Oklahoma tributary to the Red River. Oklahoma, though, has in place what Texas officials call “a panoply of expressly discriminatory state laws” that, practically speaking, block the Texas water claims.

“It is quite clear that all of the states have equal water rights,” Rothfeld told the justices, adding that “Oklahoma is now trying to back out of that bargain.”

Oklahoma, by contrast, rejects the idea each state has a right to 25 percent of the sub-basin’s water. Instead, the state insists that Texas must first obtain state approval, with the compact in place to ensure no state gets more than 25 percent of the sub-basin’s water.

“What they are asking for is unprecedented,” said attorney Lisa S. Blatt, representing Oklahoma. “There has never been a cross-border diversion, ever, under any state water compact.”

Blatt added that “Oklahoma would never have agreed to this cross-border right” had negotiators known in 1978, when the compact was completed, what Tarrant and other Texas water districts would later demand.

Under what’s called the “dormant commerce clause” of the Constitution, the Supreme Court may strike down state laws that erect barriers or discriminate against other states, but that larger constitutional question barely arose Tuesday. Justice Anthony Kennedy, in at least a partial hint of how a final decision will look, said the commerce clause “doesn’t have much to do with the case.” He said it will depend strictly on the terms of the Red River Compact itself.

“There were tough questions for both sides,” Jim Oliver, general manager of the Tarrant district, said on the Supreme Court steps following the oral arguments, adding that he “didn’t draw any conclusions” from what he heard.

As is his custom, Justice Clarence Thomas was the only one of the nine justices to stay silent and ask no questions during the argument.